Finite Group Databasebeta

← #13067549

Subgroups — #13067549

Order 1408.

310 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623128C211yesmaximal, characteristic, complemented
2C11×#447C211yesmaximal, characteristic, complemented
3#10622835C211yesmaximal, characteristic, complemented
4#10622830C211yesmaximal, characteristic, complemented
5#10622175C211yesmaximal, characteristic, complemented
6#10622108C211yesmaximal, characteristic, complemented
7#10622107C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C2×#4341—21no—
10C2×C11×D8—21no—
11C11×#121C2211yescharacteristic
12C2×C22⋊Dic11—21no—
13C2×C22⋊Dic11—21no—
14#66992—21no—
15#66992—21no—
16C2×#4323—21no—
17#66983C2211yescharacteristic
18C2×Dic11⋊C4C2211yescharacteristic
19#66949—21no—
20#66937—21no—
21#66931—21no—
22C11×#102—21no—
23C11×C22⋊C8C2211yescharacteristic
24#66896—21no—
25C11⋊#95C2211yescharacteristic
26C22⋊(C11⋊C8)C2211yescharacteristic
27C24×C11—21no—
28C2×D4×C11—21no—
29C2×D4×C11—21no—
30C2×D4×C11—21no—
31C2×D4×C11—42no—
32C2×D4×C11D411yescharacteristic
33C22×C4×C11C2311yescharacteristic
34C2×C22⋊D11—21no—
35C2×C22⋊D11—21no—
36C2×C22⋊D11—21no—
37C22×Dic11—21no—
38C22×Dic11—21no—
39C22×Dic11D411yescharacteristic
40C22×Dic11D411yescharacteristic
41#4341—42no—
42#4341—42no—
43C2×D44D411yescharacteristic
44C2×C4×D11—21no—
45C2×Dic22—21no—
46C11×D8—42no—
47C2×C8×C11—21no—
48C11×C4⋊C4D411yescharacteristic
49C11×C22⋊C4—21no—
50C22⋊Dic11—21no—
51C22⋊Dic11—42no—
52C22⋊Dic11—42no—
53#4323—42no—
54(C2×D11)⋊C4—21no—
55(C2×D11)⋊C4—21no—
56C4⋊Dic11D411yescharacteristic
57Dic11⋊C4—21no—
58Dic11⋊C4—21no—
59Dic11⋊C4—21no—
60C2×C11⋊C8—21no—
61#1598—111nomaximal, Sylow
62C23×C11—22no—
63C23×C11—21no—
64C23×C11—41no—
65C23×C11—41no—
66C23×C11—41no—
67C23×C11—41no—
68C23×C11—41no—
69C23×C11—41no—
70C23×C11C2×D411yescharacteristic
71C22×D11—21no—
72D4×C11—22no—
73D4×C11—22no—
74D4×C11—41no—
75D4×C11—41no—
76D4×C11—41no—
77D4×C11—41no—
78D4×C11—41no—
79C2×C4×C11—21no—
80C2×C4×C11—41no—
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C22⋊D11—42no—
84C22⋊D11—41no—
85C22⋊D11—41no—
86C22⋊D11—81no—
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11—21no—
91C2×Dic11—42no—
92C2×Dic11—41no—
93C2×Dic11—41no—
94C2×Dic11—41no—
95C2×Dic11—41no—
96C2×Dic11D812yescomplemented
97D44—41no—
98C4×D11—42no—
99Dic22—42no—
100C8×C11—41no—
101C11⋊C8—41no—
102#537—111no—
103#447—111no—
104#447D1111yescharacteristic, complemented
105#394—111no—
106#327—111no—
107#327—111no—
108#324—111no—
109C22×C11—21no—
110C22×C11—21no—
111C22×C11—42no—
112C22×C11—42no—
113C22×C11—41no—
114C22×C11—41no—
115C22×C11—42no—
116C22×C11—41no—
117C22×C11—81no—
118C22×C11—81no—
119C22×C11—81no—
120C22×C11—81no—
121C22×C11#12011yescharacteristic
122C22×C11C2×D811yescharacteristic
123C22×C11AGL(1,ℤ/8)11yescharacteristic
124C2×D11—41no—
125C2×D11—41no—
126C2×D11—41no—
127C4×C11—21no—
128C4×C11—21no—
129C4×C11—41no—
130Dic11—22no—
131Dic11—41no—
132Dic11—41no—
133Dic11—81no—
134C2×#41—221no—
135C22×D4C2×D1111yescharacteristic
136C2×D8—21no—
137C2×D8—221no—
138C22⋊Q8—221no—
139C22⋊Q8—221no—
140#121—111no—
141#121—221no—
142#121—221no—
143#121—221no—
144#121C2×D1111yescharacteristic
145C2×C4⋊C4—111no—
146C2×C22⋊C4—221no—
147C2×C22⋊C4—221no—
148#102—21no—
149#102—221no—
150C22⋊C8—111no—
151C22⋊C8C2×D1111yescharacteristic
152#95—111no—
153C2×C11—21no—
154C2×C11—21no—
155C2×C11—81no—
156C2×C11—82no—
157C2×C11#44711yescharacteristic
158C2×C11#45411yescharacteristic
159C2×C11B(4,𝔽2)11yescharacteristic
160D11—81no—
161C24—21no—
162#41—442no—
163#41—442no—
164C2×Q8—221no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—42no—
169C2×D4—111no—
170C2×D4—221no—
171C2×D4—221no—
172C2×D4—221no—
173C2×D4C22⋊D1111yescharacteristic
174C22×C4—111no—
175C22×C4—111no—
176C22×C4—221no—
177C22×C4—221no—
178C22×C4—221no—
179C22×C4C22×D1111yescharacteristic
180D8—42no—
181D8—442no—
182C2×C8—21no—
183C2×C8—221no—
184C4⋊C4—111no—
185C4⋊C4—221no—
186C4⋊C4—221no—
187C4⋊C4—221no—
188C4⋊C4C22⋊D1111yescharacteristic
189C22⋊C4—21no—
190C22⋊C4—221no—
191C22⋊C4—221no—
192C22⋊C4—221no—
193C22⋊C4—442no—
194C22⋊C4—442no—
195C11#159811yescharacteristic, complemented, Sylow
196C23—22no—
197C23—21no—
198C23—41no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23—41no—
203C23—41no—
204C23—221no—
205C23D4×D1111yescharacteristic
206Q8—442no—
207D4—22no—
208D4—22no—
209D4—41no—
210D4—41no—
211D4—41no—
212D4—41no—
213D4—41no—
214D4—441no—
215D4—442no—
216D4—441no—
217D4—441no—
218D4—881no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—112no—
222C2×C4—221no—
223C2×C4—221no—
224C2×C4—221no—
225C2×C4—221no—
226C2×C4—442no—
227C2×C4—442no—
228C2×C4—441no—
229C2×C4—441no—
230C2×C4—441no—
231C2×C4—441no—
232C2×C4D4×D1111yescharacteristic
233C2×C4C2×C22⋊D1111yescharacteristic
234C8—41no—
235C8—441no—
236C22—21no—
237C22—21no—
238C22—42no—
239C22—42no—
240C22—41no—
241C22—41no—
242C22—42no—
243C22—41no—
244C22—81no—
245C22—81no—
246C22—81no—
247C22—81no—
248C22—441no—
249C22—441no—
250C22—441no—
251C22D8×D1111yescharacteristic
252C22#6696411yescharacteristic
253C22#6699011yescharacteristic
254C4—21no—
255C4—21no—
256C4—41no—
257C4—222no—
258C4—441no—
259C4—441no—
260C4—881no—
261C2—21no—
262C2—21no—
263C2—82no—
264C2—81no—
265C2—881no—
266C2#1062264511yescharacteristic
267C2#1062276911yescharacteristic
268C2#1062281411yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#447C2
socleC22×C11#120
hypercenter#447D11
hypocenterC11#1598
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10623128C2semidirect
2. C11×#447C2semidirect
3. #10622835C2semidirect
4. #10622830C2semidirect
5. #10622175C2semidirect
6. #10622108C2semidirect
7. #10622107C2semidirect
96. C2×Dic11D8semidirect
104. #447D11semidirect
195. C11#1598semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#106231282
C11×#4472
#106228352
#106228302
#106221752
#106221082
#106221072
#159811